# LightOJ 1038 Race to 1 Again expectation of memorizing dp

Source: Internet
Author: User

LightOJ 1038 Race to 1 Again expectation of memorizing dp

1038-Race to 1 Again
 PDF (English) Statistics Forum
 Time Limit: 2 second (s) Memory Limit: 32 MB

Rimi learned a new thing about integers, which is-any positive integer greater1Can be divided by its divisors. So, he is now playing with this property. He selects a numberN. And he callthisD.

In each turn he randomly chooses a divisorD (1 to D). Then he dividesDBy the number to obtain newD. He repeats this procedureDBecomes1. What is the expected number of moves requiredNTo become1.

Input

Input starts with an integerT (≤ 10000), Denoting the number of test cases.

Each case begins with an integerN (1 ≤ N ≤ 105).

Output

For each case of input you have to print the case number and the expected value. Errors less10-6Will be ignored.

 Sample Input Output for Sample Input 31250 Case 1: 0Case 2: 2.00Case 3: 3.0333333333

After the equation is written, it is found that dp [n] = *** + dp [n] * C,

Moving dp [n] to one side is a common recursive formula.

```#include

#include#include

#include

using namespace std;#define N 100005double dp[N];int main(){    dp[1] = 0;    dp[2] = 2;    for(int i = 3; i < N; i++) {        dp[i] = 0;        int tmp = 0;        for(int j = 1; j*j <= i; j++)        {            if(i % j == 0)            {                dp[i] += dp[j];                tmp++;                if(j != i/j && i/j != i)                {                    dp[i] += dp[i/j];                    tmp++;                }            }        }        dp[i] = ( dp[i] + tmp+1)/tmp;    }    int n, Cas=1, T, i; scanf("%d",&T);    while(T--)    {        scanf("%d", &n);        printf("Case %d: %.10f\n", Cas++, dp[n]);    }    return 0;}

```

Related Keywords:
Related Article

The content source of this page is from Internet, which doesn't represent Alibaba Cloud's opinion; products and services mentioned on that page don't have any relationship with Alibaba Cloud. If the content of the page makes you feel confusing, please write us an email, we will handle the problem within 5 days after receiving your email.

If you find any instances of plagiarism from the community, please send an email to: info-contact@alibabacloud.com and provide relevant evidence. A staff member will contact you within 5 working days.

## A Free Trial That Lets You Build Big!

Start building with 50+ products and up to 12 months usage for Elastic Compute Service

• #### Sales Support

1 on 1 presale consultation

• #### After-Sales Support

24/7 Technical Support 6 Free Tickets per Quarter Faster Response

• Alibaba Cloud offers highly flexible support services tailored to meet your exact needs.